Question

In a survey of 100 students, the number of students studying various languages is found as: English only 18, English but not Hindi 23; English and Sanskrit 8; Sanskrit and Hindi 8, English 26, Sanskrit 48 and No language 24. Find:-
a) How many students are studying Hindi?
b) How many students are studying both English and Hindi?

Answer 1

Hint: We are going to find the solution for this question using a venn diagram. But before finding the solution, we must know what a ‘venn diagram’. It is explained below:-
A Venn diagram is a diagram that shows all possible logical relations between a finite collection of different sets.
To solve this question, we must divide the students studying different subjects into different sets, such as:-
1. English as ‘E’
2. Hindi as ‘H’
3. Sanskrit as ‘S’

Complete step-by-step answer:

Here is the venn diagram for the question:-

Total number of students surveyed = 100
Total number of students studying only English = 18
Total number of students studying English but not Hindi = 23 – 18 = 5
Total number of students studying English and Sanskrit = 8 – 5 =3
Total number of students studying Sanskrit and Hindi = 8 – 3 = 5
Total number of students studying only Sanskrit = 48 – (5+3+5)
                                                                                                                   = 48 – 13 = 35
Total number of students not studying any language = 24
a).Total number of students studying Hindi only = 100 – (18+5+5+3+35)

                                                                                                    = 100 – 66 = 34

b).Total number of students studying English and Hindi = 100 – (66+34)

                                                                                                    = 0

So, the number of students who are studying only Hindi are 34, and the number of students who are studying Hindi and English are 0.

Note: The solution of this question has been derived from the venn diagram above. There is no other way to go about this question as this question can be done only through venn diagrams otherwise the answer would come out to be a wrong one.